Do it in the spring when they are starting to grow. They are dormant now and best left alone.

Which succulents are you talking about, Wells? Some species come out of dormancy at lower temperatures and light levels than others. Those from Mediterranean climates, such as most members of the Crassula family, can be repotted in fairly early spring. Those from dry subtropical climates, with summer rain, should wait until nearly midsummer before being repotted.
Also, increasing the pot size too much when repotting will greatly increase the risk of root rot.

Don't use ordinary potting compost when you do it - they need a well draining gritty compost. Keep them pretty dry until early spring.

Repot when your succulent looks too big or if you want a change. Eventually they will break out of the pot on their own. New plants can be readily propagated from leaf or stem cuttings.

I grow a small collection of Aeonium, and these require water during the winter as long as they are still growing (which mine are). They don’t seem to want to stop, but when they do, then I can allow them to dry out more and repot any that are crammed. Mind you, I repotted some in late summer and they were fine.

Aeoniums are from Mediterranean climates, so they grow naturally in the winter. That is why I was asking Wells what kind of succulents they had.